Generating lithography design information for non-rectilinear features, such as circles and curves, can be performed by approximating such features using with piecewise linear (PWL) approximations) with a number of small, straight, rectilinear lines. Such approximations can cause significant performance, accuracy, and data size issues when applied to curvilinear surfaces. Accordingly, there is ample opportunity for improvements to methods for the design, analysis, and manufacture of non-rectilinear features.